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Gauss Multiplication Formula

(2n\pi)^{(n-1)/2}n^{1/2-nz}\Gamma(nz) = \Gamma(z)\Gamma(z+{\... n}}) = \prod_{k=0}^{n-1} \Gamma\left({z+{k\over n}}\right),

where $\Gamma(z)$ is the Gamma Function.

See also Gamma Function, Legendre Duplication Formula, Polygamma Function


Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 256, 1972.

© 1996-9 Eric W. Weisstein